如何绘制不同颜色的蓝色贝塞尔曲线的每一段？
How to draw each section of the blue Bezier curves with different color?
这是我在下面画的Bezier curves，但是它由Quadratic curves的许多子集连接在一起形成一条从P0到P6的贝塞尔曲线。从 P0 到 M0 绘制了一条曲线，从 M0 到 M1 绘制了另一条曲线，依此类推，如下所示。我需要用不同的颜色显示每条曲线，请问有什么帮助吗？
我期待如下所示的内容，不完全相同，但想法相同
这是贝塞尔曲线的Python代码：
import numpy as np
import scipy.special
import matplotlib.pyplot as plt
def calc_bezier_path(control_points, n_points=100):
"""
Compute bezier path (trajectory) given control points.
:param control_points: (numpy array)
:param n_points: (int) number of points in the trajectory
:return: (numpy array)
"""
traj = []
for t in np.linspace(0, 1, n_points):
traj.append(bezier(t, control_points))
return np.array(traj)
def bernstein_poly(n, i, t):
"""
Bernstein polynom.
:param n: (int) polynom degree
:param i: (int)
:param t: (float)
:return: (float)
"""
return scipy.special.comb(n, i) * t ** i * (1 - t) ** (n - i)
def bezier(t, control_points):
"""
Return one point on the bezier curve.
:param t: (float) number in [0, 1]
:param control_points: (numpy array)
:return: (numpy array) Coordinates of the point
"""
n = len(control_points) - 1
return np.sum([bernstein_poly(n, i, t) * control_points[i] for i in range(n + 1)], axis=0)
def line_bezier(visx, visy, control, mod="nothing"):
vis = np.column_stack((visx,visy))
path_x, path_y = np.array([]),np.array([])
setting = {"nothing":[len(vis)-2, 1, 1], "start":[len(vis)-1, 0, 0], "end":[len(vis)-1, 1, 0], "both":[len(vis), 0, -1]}
epoch = setting[mod][0]
start = setting[mod][1]
end = setting[mod][2]
if len(vis) > 2:
current_control = vis[0]
for x in range(epoch):
if x != (epoch-1):
for y in control:
if y == control[0]:
mid_control = [(vis[x+start,0]+(vis[x+(start+1),0]-vis[x+start,0])*y), (vis[x+start,1]+(vis[x+(start+1),1]-vis[x+start,1])*y)]
plt.annotate(f"M{x}", mid_control)
bezier_line = calc_bezier_path(np.array([current_control,vis[x+start], mid_control]))
path_x = np.append(path_x, bezier_line.T[0])
path_y = np.append(path_y, bezier_line.T[1])
current_control = mid_control
else:
mid_control = [(vis[x+start,0]+(vis[x+(start+1),0]-vis[x+start,0])*y), (vis[x+start,1]+(vis[x+(start+1),1]-vis[x+start,1])*y)]
plt.annotate(f"M{x}", mid_control)
bezier_line = calc_bezier_path(np.array([current_control, mid_control]))
path_x = np.append(path_x, bezier_line.T[0])
path_y = np.append(path_y, bezier_line.T[1])
current_control = mid_control
else:
if mod == "end" or mod == "both":
bezier_line = calc_bezier_path(np.array([current_control, vis[x+(end+1)]]))
else:
bezier_line = calc_bezier_path(np.array([current_control, vis[x+end], vis[x+(end+1)]]))
path_x = np.append(path_x, bezier_line.T[0])
path_y = np.append(path_y, bezier_line.T[1])
else:
path_x, path_y = visx, visy
return path_x, path_y
visx, visy = [1,2,10,15,20,25,21], [0,5,1,4,2,3,3]
control = [0.25,0.57]
path_x, path_y = line_bezier(visx, visy, control,mod="end")
plt.plot(path_x, path_y)
plt.plot(visx, visy, "--o")
for xy in range(len(visx)):
plt.annotate(f"P{xy}", [visx[xy], visy[xy]])
plt.show()
目前，您正在将贝塞尔曲线连接在一起（使用 path = np.append(path, bezier)。如果您另外创建一个列表（例如 line_collection）来保存贝塞尔曲线的每个部分，您可以单独绘制它们之后：
import numpy as np
import scipy.special
import matplotlib.pyplot as plt
def calc_bezier_path(control_points, n_points=100):
"""
Compute bezier path (trajectory) given control points.
:param control_points: (numpy array)
:param n_points: (int) number of points in the trajectory
:return: (numpy array)
"""
traj = []
for t in np.linspace(0, 1, n_points):
traj.append(bezier(t, control_points))
return np.array(traj)
def bernstein_poly(n, i, t):
"""
Bernstein polynom.
:param n: (int) polynom degree
:param i: (int)
:param t: (float)
:return: (float)
"""
return scipy.special.comb(n, i) * t ** i * (1 - t) ** (n - i)
def bezier(t, control_points):
"""
Return one point on the bezier curve.
:param t: (float) number in [0, 1]
:param control_points: (numpy array)
:return: (numpy array) Coordinates of the point
"""
n = len(control_points) - 1
return np.sum([bernstein_poly(n, i, t) * control_points[i] for i in range(n + 1)], axis=0)
def line_bezier(visx, visy, control, mod="nothing"):
vis = np.column_stack((visx,visy))
path_x, path_y = np.array([]),np.array([])
setting = {"nothing":[len(vis)-2, 1, 1], "start":[len(vis)-1, 0, 0], "end":[len(vis)-1, 1, 0], "both":[len(vis), 0, -1]}
epoch = setting[mod][0]
start = setting[mod][1]
end = setting[mod][2]
## create a new list to hold the line segments
line_collection=[]
if len(vis) > 2:
current_control = vis[0]
for x in range(epoch):
if x != (epoch-1):
for y in control:
if y == control[0]:
mid_control = [(vis[x+start,0]+(vis[x+(start+1),0]-vis[x+start,0])*y), (vis[x+start,1]+(vis[x+(start+1),1]-vis[x+start,1])*y)]
plt.annotate(f"M{x}", mid_control)
bezier_line = calc_bezier_path(np.array([current_control,vis[x+start], mid_control]))
path_x = np.append(path_x, bezier_line.T[0])
path_y = np.append(path_y, bezier_line.T[1])
## append the segment to the list
line_collection.append(bezier_line)
current_control = mid_control
else:
mid_control = [(vis[x+start,0]+(vis[x+(start+1),0]-vis[x+start,0])*y), (vis[x+start,1]+(vis[x+(start+1),1]-vis[x+start,1])*y)]
plt.annotate(f"M{x}", mid_control)
bezier_line = calc_bezier_path(np.array([current_control, mid_control]))
path_x = np.append(path_x, bezier_line.T[0])
path_y = np.append(path_y, bezier_line.T[1])
## append the segment to the list
line_collection.append(bezier_line)
current_control = mid_control
else:
if mod == "end" or mod == "both":
bezier_line = calc_bezier_path(np.array([current_control, vis[x+(end+1)]]))
else:
bezier_line = calc_bezier_path(np.array([current_control, vis[x+end], vis[x+(end+1)]]))
path_x = np.append(path_x, bezier_line.T[0])
path_y = np.append(path_y, bezier_line.T[1])
## append the segment to the list:
line_collection.append(bezier_line)
else:
path_x, path_y = visx, visy
return path_x, path_y, line_collection ## return the line_collection here
visx, visy = [1,2,10,15,20,25,21], [0,5,1,4,2,3,3]
control = [0.25,0.57]
path_x, path_y, line_collection = line_bezier(visx, visy, control,mod="end") ## init the line_collection
## iterate over list elements
for line_seg in line_collection:
plt.plot(line_seg.T[0],line_seg.T[1],linestyle="solid",linewidth=5,alpha=.5,zorder=10)
# plt.plot(path_x, path_y) ## dont need to plot this now
plt.plot(visx, visy, "--o")
for xy in range(len(visx)):
plt.annotate(f"P{xy}", [visx[xy], visy[xy]])
plt.show()
产量：
这是我在下面画的Bezier curves，但是它由Quadratic curves的许多子集连接在一起形成一条从P0到P6的贝塞尔曲线。从 P0 到 M0 绘制了一条曲线，从 M0 到 M1 绘制了另一条曲线，依此类推，如下所示。我需要用不同的颜色显示每条曲线，请问有什么帮助吗？
我期待如下所示的内容，不完全相同，但想法相同
这是贝塞尔曲线的Python代码：
import numpy as np
import scipy.special
import matplotlib.pyplot as plt
def calc_bezier_path(control_points, n_points=100):
"""
Compute bezier path (trajectory) given control points.
:param control_points: (numpy array)
:param n_points: (int) number of points in the trajectory
:return: (numpy array)
"""
traj = []
for t in np.linspace(0, 1, n_points):
traj.append(bezier(t, control_points))
return np.array(traj)
def bernstein_poly(n, i, t):
"""
Bernstein polynom.
:param n: (int) polynom degree
:param i: (int)
:param t: (float)
:return: (float)
"""
return scipy.special.comb(n, i) * t ** i * (1 - t) ** (n - i)
def bezier(t, control_points):
"""
Return one point on the bezier curve.
:param t: (float) number in [0, 1]
:param control_points: (numpy array)
:return: (numpy array) Coordinates of the point
"""
n = len(control_points) - 1
return np.sum([bernstein_poly(n, i, t) * control_points[i] for i in range(n + 1)], axis=0)
def line_bezier(visx, visy, control, mod="nothing"):
vis = np.column_stack((visx,visy))
path_x, path_y = np.array([]),np.array([])
setting = {"nothing":[len(vis)-2, 1, 1], "start":[len(vis)-1, 0, 0], "end":[len(vis)-1, 1, 0], "both":[len(vis), 0, -1]}
epoch = setting[mod][0]
start = setting[mod][1]
end = setting[mod][2]
if len(vis) > 2:
current_control = vis[0]
for x in range(epoch):
if x != (epoch-1):
for y in control:
if y == control[0]:
mid_control = [(vis[x+start,0]+(vis[x+(start+1),0]-vis[x+start,0])*y), (vis[x+start,1]+(vis[x+(start+1),1]-vis[x+start,1])*y)]
plt.annotate(f"M{x}", mid_control)
bezier_line = calc_bezier_path(np.array([current_control,vis[x+start], mid_control]))
path_x = np.append(path_x, bezier_line.T[0])
path_y = np.append(path_y, bezier_line.T[1])
current_control = mid_control
else:
mid_control = [(vis[x+start,0]+(vis[x+(start+1),0]-vis[x+start,0])*y), (vis[x+start,1]+(vis[x+(start+1),1]-vis[x+start,1])*y)]
plt.annotate(f"M{x}", mid_control)
bezier_line = calc_bezier_path(np.array([current_control, mid_control]))
path_x = np.append(path_x, bezier_line.T[0])
path_y = np.append(path_y, bezier_line.T[1])
current_control = mid_control
else:
if mod == "end" or mod == "both":
bezier_line = calc_bezier_path(np.array([current_control, vis[x+(end+1)]]))
else:
bezier_line = calc_bezier_path(np.array([current_control, vis[x+end], vis[x+(end+1)]]))
path_x = np.append(path_x, bezier_line.T[0])
path_y = np.append(path_y, bezier_line.T[1])
else:
path_x, path_y = visx, visy
return path_x, path_y
visx, visy = [1,2,10,15,20,25,21], [0,5,1,4,2,3,3]
control = [0.25,0.57]
path_x, path_y = line_bezier(visx, visy, control,mod="end")
plt.plot(path_x, path_y)
plt.plot(visx, visy, "--o")
for xy in range(len(visx)):
plt.annotate(f"P{xy}", [visx[xy], visy[xy]])
plt.show()
目前，您正在将贝塞尔曲线连接在一起（使用 path = np.append(path, bezier)。如果您另外创建一个列表（例如 line_collection）来保存贝塞尔曲线的每个部分，您可以单独绘制它们之后：
import numpy as np
import scipy.special
import matplotlib.pyplot as plt
def calc_bezier_path(control_points, n_points=100):
"""
Compute bezier path (trajectory) given control points.
:param control_points: (numpy array)
:param n_points: (int) number of points in the trajectory
:return: (numpy array)
"""
traj = []
for t in np.linspace(0, 1, n_points):
traj.append(bezier(t, control_points))
return np.array(traj)
def bernstein_poly(n, i, t):
"""
Bernstein polynom.
:param n: (int) polynom degree
:param i: (int)
:param t: (float)
:return: (float)
"""
return scipy.special.comb(n, i) * t ** i * (1 - t) ** (n - i)
def bezier(t, control_points):
"""
Return one point on the bezier curve.
:param t: (float) number in [0, 1]
:param control_points: (numpy array)
:return: (numpy array) Coordinates of the point
"""
n = len(control_points) - 1
return np.sum([bernstein_poly(n, i, t) * control_points[i] for i in range(n + 1)], axis=0)
def line_bezier(visx, visy, control, mod="nothing"):
vis = np.column_stack((visx,visy))
path_x, path_y = np.array([]),np.array([])
setting = {"nothing":[len(vis)-2, 1, 1], "start":[len(vis)-1, 0, 0], "end":[len(vis)-1, 1, 0], "both":[len(vis), 0, -1]}
epoch = setting[mod][0]
start = setting[mod][1]
end = setting[mod][2]
## create a new list to hold the line segments
line_collection=[]
if len(vis) > 2:
current_control = vis[0]
for x in range(epoch):
if x != (epoch-1):
for y in control:
if y == control[0]:
mid_control = [(vis[x+start,0]+(vis[x+(start+1),0]-vis[x+start,0])*y), (vis[x+start,1]+(vis[x+(start+1),1]-vis[x+start,1])*y)]
plt.annotate(f"M{x}", mid_control)
bezier_line = calc_bezier_path(np.array([current_control,vis[x+start], mid_control]))
path_x = np.append(path_x, bezier_line.T[0])
path_y = np.append(path_y, bezier_line.T[1])
## append the segment to the list
line_collection.append(bezier_line)
current_control = mid_control
else:
mid_control = [(vis[x+start,0]+(vis[x+(start+1),0]-vis[x+start,0])*y), (vis[x+start,1]+(vis[x+(start+1),1]-vis[x+start,1])*y)]
plt.annotate(f"M{x}", mid_control)
bezier_line = calc_bezier_path(np.array([current_control, mid_control]))
path_x = np.append(path_x, bezier_line.T[0])
path_y = np.append(path_y, bezier_line.T[1])
## append the segment to the list
line_collection.append(bezier_line)
current_control = mid_control
else:
if mod == "end" or mod == "both":
bezier_line = calc_bezier_path(np.array([current_control, vis[x+(end+1)]]))
else:
bezier_line = calc_bezier_path(np.array([current_control, vis[x+end], vis[x+(end+1)]]))
path_x = np.append(path_x, bezier_line.T[0])
path_y = np.append(path_y, bezier_line.T[1])
## append the segment to the list:
line_collection.append(bezier_line)
else:
path_x, path_y = visx, visy
return path_x, path_y, line_collection ## return the line_collection here
visx, visy = [1,2,10,15,20,25,21], [0,5,1,4,2,3,3]
control = [0.25,0.57]
path_x, path_y, line_collection = line_bezier(visx, visy, control,mod="end") ## init the line_collection
## iterate over list elements
for line_seg in line_collection:
plt.plot(line_seg.T[0],line_seg.T[1],linestyle="solid",linewidth=5,alpha=.5,zorder=10)
# plt.plot(path_x, path_y) ## dont need to plot this now
plt.plot(visx, visy, "--o")
for xy in range(len(visx)):
plt.annotate(f"P{xy}", [visx[xy], visy[xy]])
plt.show()
产量：